Surface growth scheme for bulk reconstruction and tensor network

Abstract

We propose a surface growth approach to reconstruct the bulk spacetime geometry, motivated by Huygens'principle of wave propagation. We first construct a tensor network corresponding to a special surface growth picture with spherical symmetry and fractal feature using the one-shot entanglement distillation (OSED)method and show that the resulting tensor network is equivalent to the MERA-like tensor network, which gives a proof that the MERA-like tensor network is indeed a discretized version of the time slice of AdS spacetime, rather than just an analogy. Furthermore, we generalize the original OSED method to describe more general surface growth picture by using of surface/state correspondence and generalized RT formula, which leads to a more profound understanding for the surface growth process and provides a concrete and intuitive way for the idea of entanglement wedge reconstruction.

41 pages, 15 figures, accepted by JHEP

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• Deriving the PEE proposal from the Locking bit thread configuration
• Bending the Bruhat-Tits Tree I:Tensor Network and Emergent Einstein Equations
• Entanglement distillation toward minimal bond cut surface in tensor networks
• Thread/State correspondence: from bit threads to qubit threads
• Note on surface growth approach for bulk reconstruction
• Towards bit threads in general gravitational spacetimes
• Hyperfine Structure of Quantum Entanglement